Method of and apparatus for producing fluid gravity and density analogs and flowmeters incorporating gravitometers

ABSTRACT

Gas flowmeters for indicating total volume flow. The flowmeters incorporate gravitometers having vibration densitometers including spring metal ferromagnetic cantilevered vanes which vibrate when driven. A thermally conductive housing stores heat and equalizes the temperature between a gas of interest and air. The air is kept dry by a desiccator. The gas is circulated through a first chamber in the housing containing one vane. Air occupies a second chamber having another vane therein. Both chambers are vented to the atmosphere. The gas is circulated through the first chamber very slowly so that the pressures in both chambers are approximately equal to atmospheric. In one embodiment of the gravitometer, gravity, G, is computed in a manner similar to

United States Patent 1 1 Schlatter et a1.

[ 1 Jan. 28, 1975 [75] Inventors: Gerald Lance Schlatter; Charles Eveleigh Miller, both of Boulder, C010.

[73] Assignee: International Telephone and Telegraph Corporation, New York,

[22] Filed: June 22, 1972 [21] Appl. No.: 265,327

[5 [3.5. CI 73/32 A [51 Int. Cl. GOln 9/34 [58 Field of Search 73/32 A, 32 R, 30

[56] References Cited UNITED STATES PATENTS 1.527,?21 2/1925 Willey 73/30 1.906.985 5/1933 Marrison 310/25 X 3,002,373 10/1961 Kimmel1.... 73/30 3,117,440 1/1964 Wilner 73/32 A 3.134.035 5/1964 Grib 310/25 3.572.094 3/1971 Banks i 73/32 A 3.603.137 9/1971 Banks i 73/32 A 3.715.912 4/1971 Schlatter... 73/32 R FOREIGN PATENTS OR APPLICATIONS 9/1968 Great Britain 73/32 A Primary Examiner-James .l. Gill Attorney, Agent, or FirmA. Donald Stolzy ABSTRACT Gas flowmeters for indicating total volume flow. The flowmeters incorporate gravitometers having vibration densitometers including spring metal ferromagnetic cantilevered vanes which vibrate when driven.

A thermally conductive housing stores heat and equalizes the temperature between a gas of interest and air. The air is kept dry by a desiccator. The gas is circulated through a first chamber in the housing containing one vane. Air occupies a second chamber having another vane therein. Both chambers are vented to the atmosphere. The gas is circulated through the first chamber very slowly so that the pressures in both chambers are approximately equal to atmospheric.

In one embodiment of the gravitometer, gravity. G, is

computed in a manner similar to G =1 -DFAf,

where,

D is a constant,

F is the ratio of ambient air temperature to ambient air pressure, and

Af, is the difference between the vane frequencies.

In another embodiment, gravity is computed in a manner similar to G 1 VAtAf where,

V is a contant, and At is the reciprocal of the difference between the air vane frequency and a vacuum frequency, f,,,

f,,= 1/t when 0. Another calculation of G is made as in G 1 DFAf,

where the F factor is incorporated by using a pressure regulator with a flexible diaphragm betweena sealed dry air chamber and a third gas chamber connected from the first chamber and vented to the atmosphere through a valve controlled by the diaphragm.

44 Claims, 34 Drawing Figures PATENTED JAN 2 8 I975 SHEEI 01 [1F 16 PATEN TED JAN 2 81975 SHEET 0? or 16 0a 287 CURRNT 7'0 PHASE D6 766 7 0/2 /24 P'Arsutmmza 3882.588 snm 11 one PATENTED JAN 2 8 I975 SHEET 12W 16 PATENTEU JAN 2 8 I975 sum 15 or 16 METHOD OF AND APPARATUS FOR PRODUCING FLUID GRAVITY AND DENSITY ANALOGS AND FLOWMETERS INCORPORATING GRAVITOMETERS BACKGROUND OF THE INVENTION This invention relates to the art of fluid measurement, and more particularly, to apparatus which may be employed in densitometers, gravitometers or flowmeters.

The word gravity is hereby defined for use herein and in the claims to mean the same thing that it conventionally means in this art, i.e., it is hereby defined to mean the ratio of the density of a gas to the density of air at the same temperature and pressure. As will be explained hereinafter, the gravity of a gas is otherwise substantially independent of temperature and pressure.

In the past, it has been the practice to measure the gravity ofa gas by loading a gas tight cylinder with a gas and placing it on a balance with a gas tight cylinder of air. This apparatus is expensive and cumbersome to use. Moreover, gravity is obtained by performing a batch process which cannot run continously with flowmeter apparatus to indicate instantaneously what the rate of volume flow and the total volume flow in a pipeline is.

SUMMARY OF THE INVENTION In accordance with the present invention, an instantaneous indication of density or gravity or signals directly proportional thereto may be obtained through the use of a vibration densitometer having a spring metal cantilevered ferromagnetic vane.

Two such densitometers may be used in a gravitometer.

In accordance with the present invention, the gravitometer thereof may be used in one or more total volume or rate of volume flow flowmeters to provide an analog output signal directly proportional to rate of volume flow. The gravitometers and flowmeters of the present invention thus have a much faster speed of response and are more accurate than gravitometers and flowmeters of the prior art.

Notwithstanding the foregoing, the gravitometers of the present invention have utility when used by themselves and not in a flowmeter. For example, the output of a gravitometer constructed in accordance with the present invention may be connected to one or more process controllers, orxto a DC. milliammeter or recorder calibrated in gravity, or any other apparatus.

Different natural gases are frequently blended to achieve a desired BTU content based on the gas gravitles.

A gravity indication is thus useful in estimating the BTU content of natural gas. It can be used in determining performance under gas delivery contracts specifying BTU content. Further, estimated BTU content is also frequently used for billing purposes.

As will be understood from the foregoing, automatic process controllers can be operated from the gravitometers of the present invention to maintain automatically any desired gravity or BTU content.

According to another feature of the invention, gravity is obtained from the beat frequency analog of a pair of vanes. An air density analog is obtained by deriving the reciprocal of a difference frequency analog which is directly proportional to the vane frequency of a vacuum minus the air vane frequency. Alternatively, a ratio of the temperature to the pressure of ambient air is obtained. If desired, a conventional phase locked loop may be employed to provide the DC. voltage analog of the beat frequency.

Another feature of the present invention resides in the unexpected use of a single power amplifier and driver coil to vibrate two vanes even though the two vanes vibrate at different frequencies.

Alternative air density analogs are provided by a gas chamber pressure control or by a T/P compensator.

Other features of the invention reside in the use of efficient apparatus for temperature equalization, desiccator apparatus to keep the air dry, and resilient mounts for isolation from extraneous vibrational interference.

The above-described and other advantages of the present invention will be better understood from the following detailed description when considered in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS In the drawings which are to be regarded as merely illustrative:

FIG. 1 is a diagrammatic view of a flowmeter;

FIG. 2 is a schematic diagram of a pickup shown in FIG. 1;

FIG. 3 is a graph of a group of waveforms characteristic of the operation of the invention shown in FIG. 1;

FIG. 4 is a diagrammatic view of a flowmeter constructed in accordance with an alternative embodiment of the present invention;

FIG. 5 is a diagrammatic view of a gravitometer;

FIG. 6 is a top plan view of a twin cell assembly indicated diagrammatically in FIG. 5;

FIG. 7 is a vertical sectional view taken on the line 7-7 through a mounting bolt shown in FIG. 6;

FIG. 8 is a vertical sectional view taken on the line 88 shown in FIG. 6;

FIG. 9 is a horizontal sectional view taken on the line 9-9 shown in FIG. 8;

FIG. 10 is a vertical sectional view taken on the line 10-10 shown in FIG. 6;

FIG. 11 is a vertical sectional view taken on the line 11-11 shown in FIG. 10;

FIG. 12 is a vertical sectional view taken on the line 12-12 shown in FIG. 6;

FIG. 13 is a horizontal sectional view taken on the line 13-13 shown in FIG. 12;

FIG. 14 is a perspective view of a ferromagnetic rod shown in FIGS. 6, 10, 11 and 12;

FIG. 15 is a vertical sectional view taken on the line 15-15 shown in FIG. 6; i

FIG. 16 is a horizontal sectional view taken on the line 16-16 shown in FIG. 15;

FIG. 17 is a schematic diagram of a portion of the circuit shown in FIG. 5;

FIG. 18 is a diagrammatic view of an alternative gravitometer constructed in accordance with the present invention;

FIG. 19 is a schematic diagram of an analog adder shown in FIG. 18;

FIG. 20 is a schematic diagram of portions of the blocks shown in FIG. 18;

FIG. 21 is a graph ofa group of waveforms characteristic of the operation of the gravitometer alternative embodiment of FIG. 18;

FIG. 22 is a block diagram of an alternative embodiment of the present invention;

FIG. 23 is a rear elevational view of a gravity cell shown in FIG. 22;

FIG. 24 is a top plan view of the cell shown in FIG. 23;

FIG. 25 is a side elevational view of the cell shown in FIG. 23;

FIG. 26 is a transverse sectional view of the cell taken on the line 26-26 shown in FIG. 23;

FIG. 27 is a vertical sectional view of the cell taken on the line 27-27 shown in FIG. 24;

FIG. 28 is a longitudinal sectional view of a conventional pressure relay;

FIG. 29 is a block diagram further illustrating the embodiment of the invention shown in FIG. 22;

FIG. 30 is a schematic diagram of a frequency-tovoltage converter;

FIGS. 31 and 32 are schematic diagrams of still another embodiment of the present invention; and

FIGS. 33 and 34 are graphs of a group of waveforms characteristic of the operation of the embodiment shown in FIGS. 31 and 32.

DESCRIPTION OF THE PREFERRED EMBODIMENTS THE FLOWMETER OF FIG. 1

It is well known in the prior art that the total flow I Q dt where t is time and Q is the volume rate of gas flow per unit time, Q being measured in standard cubic feet. This standard cubic feet (at, for example, 14.7 pounds/cubic feet pressure and 68 F.) of a gas in a pipeline may be calculated from the following equation (1) defining mass flow rate Q.

Q K PA P/TG where,

P is the static pressure in a pipeline 30 shown in FIG.

AP is the differential pressure across an orifice 32. T is the absolute temperature of the gas, and G is the gravity of the gas. The gravity, G, of a gas is defined by G Pa/Pa which is equal to a constant. Hence,

PV MRT where,

P is pressure, V is volume, M is mass, R is the gas constant, and

T is absolute temperature. If p is density, then p M/V Thus, combining (4) and (5),

p K P/T where,

K, HR

Equations (8) and (9) are analogous to (6) for a gas. g, of interest and air, a.

Pg 18 a/Tu Equation (11) thus indicates that G is truly independent of which set of temperature and pressure conditions are selected.

Equation (1) may be proven as follows. The flow. 0,,

through an orifice is Ox z 8 H0 tlZ) where,

K is a constant,

A is the orifice area,

g is acceleration due to the earths gravity, and

Hg is the differential pressure head in feet across the orifice. To convert the differential head to inches of air y Hnpn/ l P p K GP/T where,

P is equal to P T is equal to T and p isequal to p Substituting p p 'into (13), (14) into the resultant, one obtains Hg I-la p aT/12 K GP Substituting (15) into (12) one obtains Q, K A 2,,H,,paT/l21( GP I Thus, I

Q. 3 JHqP where,

K, K A ,l2g/12K From expression (3) aQaITa Thus,

a a/TPa Combining (17) and (20) I o K, H p aT/GP X PT /TP,

and

Q K I P AP/TG where,

K ZlTaIPa and A p is equal to H p (pressure equals height times density).

The embodiment of FIG. 1 mechanizes equation (1) for continuously indicating total volume flow in standard cubic feet.

In FIG. 1, a portion of a pipeline is indicated at 30 having a disc 31 fixed therein to provide an orifice 32. A differential pressure transducer 33 senses the difference between the pressures on opposite sides of orifice 32. A static pressure transducer 34 senses the pressure on one side of orifice 32. a temperature transducer '35 senses the temperature on one side of the orifice 32.

In FIG. 1 a multiplier 36, a multiplier 37, a divider 38 and a square root extractor 39 are provided. An output circuit 40 is connected from the output of square root extractor 39. Output circuit 40 includes a pickoff 41, a saw-tooth generator 42, an inverter 43, a burst oscillator 44, a gate 45 and a counter 46.

Differential pressure transducer 33 produces a DC. current on an output lead 47 which is directly proportional to the difference between the pressures on opposite sides of the orifice 32.

Static pressure transducer 34 produces a DC. current on an output lead 48 directly proportional to the pressure on one side of orifice 32. Temperature transducer 35 produces a DC. current on an output lead 49 directly proportional to the temperature of the gas inside pipeline portion 30 on one side of orifice 32.

A gravitometer 50 is connected from pipeline portion 30 on one side of orifice 32 to produce a DC. output current on an output lead 51 directly proportional to the gravity of the gas in pipeline portion 30.

Multiplier 36 is connected from leads 49 and 51. The output of multiplier 36 is impressed upon an output lead 52 which is connected to divider 38. Multiplier 36 then produces an output current in lead 52 which is directly proportional to the product of the output currents of temperature transducer 35 and gravitometer 50.

Multiplier 37 is connected from both of the pressure transducers 33 and 34 to divider 38. Multiplier 37 has an output lead 53, the current in which is directly proportional to the product of the current outputs of the pressure transducers 33 and 34. divider 38 has an output lead 54 which carries a DC. voltage directly proportional to the output of multiplier 37 divided by the output of multiplier 36. Divider 38 may, if desired, include a current-to-voltage converter at its output. A current-to-voltage converter, for example, may be simply a resistor connected from the output of divider 38 to ground.

Notwithstanding the foregoing, any component part of the invention employed to produce a current analog may be employed to produce a voltage analog.

Square root extractor 39 has an output lead 55 upon which a DC. voltage is impressed which is directly proportional to the square root of the output of divider 38.

Pickoff 41 has an output lead 56 upon which a square wave is impressed. This square wave is generated by comparing the amplitude of the saw-tooth output of generator 42 with the amplitude of the DC. voltage on lead 55.

Inverter 43 is connected over an output lead 57 to gate 45. Inverter 43 inverts the square wave output of pickoff 41.

It is to be noted that the dimensions of a square wave are conventionally vertical in volts and horizontal in time. The word square thus has no reference to any particular relationship between the amplitude and period of such a wave. The phrase square wave is, therefore, hereby defined for use herein and in the claims to mean a rectangular wave or vice versa.

Burst oscillator 44 produces output pulses at a constant rate and at a pulse repetition frequency (PRF) which is large in comparison to the PRF of the square wave appearing on inverter output lead 57. Gate 45 is opened during the positive pulses of the square wave on 

1. A gravitometer comprising: a body having first and second chambers therein to contain air and a gas of interest, respectively; first and second spring metal ferromagnetic cantilevered vanes mounted in said first and second chambers, respectively, each vane having one end fixed relative to said body and a free end opposite thereof for immersion in said air and gas, respectively, said first vane free end being positioned to vibrate back and forth in a first pair of predetermined opposite directions in said first chamber without touching said body, said second vane free end being positioned to vibrate back and forth in a second pair of predetermined opposite directions in said second chamber without touching said body, said first pair of directions being approximately parallel to the direction in which the thicknesses of both of said first and second vanes are measured, said second pair of directions being approximately parallel to the direction in which the second vane thickness is measured; driver coil means fixed relative to said body in a position to attract said vane free ends when said coil is energized; first and second piezoelectric crystals fixed relative to and contiguous to the said one end of said first and second vanes, respectively; amplifier means connected from both of said crystals to said driver coil means to impress an output signal on said driver coil means to cause said first and second vanes to vibrate continuously at respective frequencies equal to the frequencies of the output signals of said first and second crystals, respectively, said amplifier means including means to produce a sum signal directly proportional to the sum of the output signals of said crystals, said amplifier means being connected to said driver coil to impress said sum signal thereon; computer means connected from both of said crystals to produce an output signal responsive to the outputs of said crystals which is directly proportional to Io, where dIo/dG equals a constant and G Rho g/ Rho a, where Rho g is the density of said gas, and Rho a is the density of said air; and utilization means connected from said computer means to receive said output signal thereof.
 2. The invention as defined in claim 1, wherein said amplifier means includes first and second amplifiers connected from said first and second crystals, respectiVely, first and second AGC circuits connected from the respective outputs to the respective AGC inputs of said first and second amplifiers, a power amplifier having first, second and third inputs and an output, first, second and third resistors connected respectively from said first, second and third inputs to a summing junction, said first input being connected to a first junction, a fourth resistor connected from said first junction to a point of reference potential, one side of said coil being connected to said first junction, said first and second amplifier outputs being connected respectively to said second and third inputs, a capacitor and a fifth resistor connected in series in that order from said power amplifier output to said summing junction, said power amplifier output being connected to the other side of said coil.
 3. The invention as defined in claim 2, wherein offset means are provided including an auxiliary resistor connected to said summing junction to supply a substantially constant voltage thereto.
 4. The invention as defined in claim 3, wherein said offset means is adjustable to adjust the magnitude of said constant voltage.
 5. A gravitometer comprising: a body having first and second chambers therein to contain air and a gas of interest, respectively; first and second spring metal ferromagnetic cantilevered vanes mounted in said first and second chambers, respectively, each vane having one end fixed relative to said body and a free end opposite thereof for immersion in said air and gas, respectively, said first vane free end being positioned to vibrate back and forth in a first pair of predetermined opposite directions in said first chamber without touching said body, said second vane free end being positioned to vibrate back and forth in a second pair of predetermined opposite directions in said second chamber without touching said body, said first pair of directions being approximately parallel to the direction in which the thickness is of both of said first and second vanes are measured, said second pair of directions being approximately parallel to the direction in which the second vane thickness is measured; driver coil means fixed relative to said body in a position to attract said vane free ends when said coil is energized; first and second piezoelectric crystals fixed relative to and contiguous to the said one end of said first and second vanes, respectively; amplifier means connected from both of said crystals to said driver coil means to impress an output signal on said driver coil means to cause said first and second vanes to vibrate continuously at respective frequencies equal to the frequencies of the output signals of said first and second crystals, respectively, said amplifier means including means to produce a sum signal directly proportional to the sum of the output signals of said crystals, said amplifier means being connected to said driver coil to impress said sum signal thereon; sensor means for producing an output directly proportional to F, where F Ta/Pa where Ta is the temperature of ambient air, and Pa is the pressure of ambient air; computer means connected from both of said crystals and from said sensor means to produce an output signal directly proportional to I, where dI/dG is equal to a constant, and G 1 - DF Delta f1 where Delta f1 fg - fa fg is the frequency of the output signal of said second crystal, fa is the frequency of the output signal of said first crystal, and D is a constant.
 6. The invention as defined in claim 5, wherein said amplifier means includes first and second amplifiers connected from first and second crystals, respectively, first and second AGC circuits connected from the respective outputs to the respective AGC inputs of said first and second amplifiers, a power amplifier having first, second and third inputs and an output, first, second and third resistors connected respectively from said first, second and third inputs to a summing junction, said first input being connected to a first junction, a fourth resistor connected from said first junction to a point of reference potential, one side of said coil being connected to said first junction, said first and second amplifier outputs being connected respectively to said second and third inputs, a capacitor and a fifth resistor connected in series in that order from said power amplifier output to said summing junction, said power amplifier output being connected to the other side of said coil.
 7. The invention as defined in claim 6, wherein offset means are provided including an auxiliary resistor connected to said summing junction to supply a substantially constant voltage thereto.
 8. The invention as defined in claim 7, wherein said offset means is adjustable to adjust the magnitude of said constant voltage.
 9. The invention as defined in claim 8, wherein said computer means includes a main AM detector connected from the output of said power amplifier, a phase locked loop connected from said AM detector including a phase detector, a low pass filter, an amplifier and a VCO connected in succession in that order from said main AM detector, said VCO having its output connected to said phase detector, said sensor means including a potentiometer having a winding including first and second ends, and a movable wiper, said first winding end being connected from the output of said loop amplifier, said second winding end being connected to a point of reference potential, a cylinder, a piston reciprocable in said cylinder, said piston sealing a quantity of air in said cylinder, means to move said wiper on said winding at a rate directly proportional to the rate of movement of said piston relative to said cylinder as the ambient air temperature and/or pressure changes, and an output amplifier connected from said wiper to add a manually adjustable voltage of a predetermined polarity to the voltage appearing at said wiper, said output amplifier having a manually adjustable gain.
 10. A gravitometer comprising: a body having first and second chambers therein to contain air and a gas of interest, respectively; first and second spring metal ferromagnetic cantilevered vanes mounted in said first and second chambers, respectively, each vane having one end fixed relative to said body and a free end opposite thereof for immersion in said air and gas, respectively, said first vane free end being positioned to vibrate back and forth in a first pair of predetermined opposite directions in said first chamber without touching said body, said second vane free end being positioned to vibrate back and forth in a second pair of predetermined opposite directions in said second chamber without touching said body, said first pair of directions being approximately parallel to the direction in which the vane thickness of said first vane is measured, said second pair of directions being approximately parallel to the direction in which the second vane thickness is measured; driver coil means fixed relative to said body in a position to attract said vane free ends when said coil is energized; first and second piezoelectric crystals fixed relative to and contiguous to the said one end of said first and second vanes, respectively; amplifier means connected from both of said crystals to said driver coil means to impress an output signal on said driver coil means to cause said first and second vanes to vibrate continuously at respective frequencies equal to the frequencies of the output signals of said first and second crystals, respectively, said amplifier means including means to produce a sum signal directly proportional to the sum of the output signals of said crystals, said amplifier means being connected to said driver coil to impress said sum signal thereon; fo source means; and computer means connected from both of said crystals and from said source means to produce an output signal directly proportional to It, where dIt/dG a constant, G 1 - V Delta t Delta f1, V is a constant, Delta t 1/fo - fa, fo - A/B, where A and B are constants in the equation of gas density Rho for both of vanes Rho At B where t is the vane vibrational period, fa is the frequency of vibration of said first vane, Delta f1 fg - fa, and fg is the frequency of vibration of said second vane.
 11. The invention as defined in claim 10, wherein said amplifier means includes first and second amplifier connected from said first and second crystals, respectively, first and second AGC circuits connected from the respective outputs of the respective AGC inputs of said first and second amplifiers, a power amplifier having first, second and third inputs and an output, first, second and third resistors connected respectively from said first, second and third inputs to a summing junction, said first input being connected to a first junction, a fourth resistor connected from said first junction to a point of reference potential, one side of said coil being connected to said first junction, said first and second amplifier outputs being connected respectively to said second and third inputs, a capacitor and a fifth resistor connected in series in that order from said power amplifier output to said summing junction, said power amplifier output being connected to the other side of said coil.
 12. The invention as defined in claim 11, wherein offset means are provided including an auxiliary resistor connected to said summing junction to supply a substantially constant voltage thereto.
 13. The invention as defined in claim 12, wherein said offset means is adjustable to adjust the magnitude of said constant voltage.
 14. The invention as defined in claim 13, wherein said amplifier means includes first and second amplifier connected from said first and second crystals, respectively, first and second AGC circuits connected from the respective outputs to the respective AGC inputs of said first and second amplifiers, a power amplifier having first, second and third inputs and an output, first, second and third resistors connected respectively from said first, second and third inputs to a summing junction, said first input being connected to a first junction, a fourth resistor connected from said first junction to a point of reference potential, one side of said coil being connected to said first junction, said first and second amplifier outputs being connected respectively to said second and third inputs, a capacitor and a fifth resistor connected in series in that order from said power amplifier output to said summing junction, said power amplifier output being connected to the other side of said coil.
 15. The invention as defined in claim 14, wherein offset means are provided including an auxiliary resistor connected to said summing junction to supply a substantially constant voltage thereto.
 16. The invention as defined in claim 15, wherein said offset means is adjustable to adjust the magnitude of said constant voltage.
 17. The invention as defined in claim 16, wherein said computer means includes a main AM detector connected from the output of said power amplifier, a phase locked loop connected from said AM detector including a phase detector, a low pass filter, an amplifier and a VCO connected in succession in that order from said main AM detector, said VCO having its output connected to said phase detector, said source means including a crystal oscillator, an analog adder connected from said oscillator and said first crystal, an auxiliary AM detector connected from said adder, a square wave generator connected from said auxiliary AM detector, and output means connected from the outputs of said square wave generAtor and said loop amplifier for producing a D.C. output voltage directly proportional to V Delta t Delta f1, where Delta t is the period of the output signal of said square wave generator, and the output of said loop amplifier is directly proportional to Delta f1.
 18. The invention as defined in claim 17, wherein said output means includes a first switch, an integrator, a second switch, an output circuit and utilization means connected in succession in that order from said square wave generator, said first switch also being connected from said loop amplifier to pass the output signal thereof to said integrator during the occurrence of an output pulse from said square wave generator, a timing circuit connected from said square wave generator to said integrator and to said second switch, said timing circuit causing said second switch to sample the output of said integrator after the trailing edge of each of said generator pulses and before the leading edge of each next succeeding generator pulse, said timing circuit causing said integrator to reset after each sampling and before the occurence of the next succeeding generator leading pulse edge, said output circuit including a sampling capacitor connected from the input thereof to a point of reference potential, said output circuit including an output amplifier connected from said second switch to add a manually adjustable voltage of a predetermined polarity to the voltage appearing at the output of said second switch, said output amplifier having a manually adjustable gain.
 19. The invention as defined in claim 1, wherein said sum signal has an amplitude directly proportional to Rho f, where Rho f 2E2 sin (x + Mu )/2 cos (x - Mu )/2 where 2E2 is the peak amplitude of the carrier, x N omega wt/2, Mu N omega vt/2, where omega 6.28, t is time, N is one of the integers 1 and 2, w is the frequency of the output signal of the gas crystal, for example, and v is the frequency of the output signal of the air crystal, for example.
 20. A gas gravitometer comprising: a gas tight source of a sample gas under pressure; first thermally conductive means providing a gas tight sealed chamber of dry air; second thermally conductive means in contact with said first means and providing a gas tight sample chamber having an inlet and an outlet; a pressure relay connected from said source and said sealed chamber to said sample chamber inlet, said pressure relay having means to pass varying amounts of said sample gas from said source to said sample chamber; an atmospheric vent; bleed means connected from said sample chamber outlet to said vent, said bleed means providing a constriction to flow of said sample gas therethrough sufficiently small that said pressure relay holds the pressure of said sample gas in said sample chamber equal to the pressure of said dry air in said sealed chamber; first and second cantilevered leaf spring ferromagnetic vanes sealed in said sealed and gas chambers, respectively; first and second piezoelectric crystals fixed relative to the fixed ends of said first and second vanes, respectively; first and second amplifiers connected from said first and second crystals, respectively; a first AGC circuit connected from the output of said first amplifier to the AGC input of said first amplifier; a second AGC circuit connected from the output of said second amplifier to the AGC input thereof, said AGC circuits causing the peak amplitudes at the outputs of said first and second amplifiers to be substantially equal; a power amplifier means connected from the outputs of both said first and second amplifiers to produce an output signal directly proportional to the algebraic sum of the amplitudes of the output signals of said first and second amplifiers; a driver coil connected from said power amplifier means to vibrate both of said vanes simultaneouSly; output means connected from the output of said power amplifier means to produce a signal of a magnitude directly proportional to the difference between the frequencies of the signals appearing at the outputs of said first and second amplifiers; and utilization means connected from said output means.
 21. The invention as defined in claim 20, wherein said output means includes an AM detector, a square wave generator, and a frequency-to-voltage converter connected in succession in that order from the output of said power amplifier means to the input of said utilization means.
 22. The invention as defined in claim 21, wherein said converter includes an auxiliary amplifier having its output connected to the input of said utilization means, a first resistor and a second resistor connected in series in that order from said square wave generator to the input of said auxiliary amplifier, a feedback capacitor connected from the output of said auxiliary amplifier to the junction between said resistors, and a parallel capacitor connected from said auxiliary amplifier input to a point of reference potential.
 23. The invention as defined in claim 22, wherein said utilization means includes a voltmeter calibrated in G, where G Rho g/ Rho a, Rho g is the density of said gas in said gas chamber, and Rho a is the density of said dry air in said sealed chamber.
 24. A gas gravitometer comprising: a gas tight source of a sample gas under pressure; first thermally conductive means providing a gas tight sealed chamber of dry air; second thermally conductive means in contact with said first means and providing a gas tight sample chamber having an inlet and an outlet; a pressure relay connected from said source and said sealed chamber to said sample chamber inlet, said pressure relay having third means to pass varying amounts of said sample gas from said source to said sample chamber; an atmospheric vent; bleed means connected from said sample chamber outlet to said vent, said bleed means providing a constriction to flow of said sample gas therethrough sufficiently small that said pressure relay holds the pressure of said sample gas in said sample chamber equal to the pressure of said dry air in said sealed chamber first and second cantilevered leaf spring ferromagnetic vanes sealed in said sealed and gas chambers, respectively; first and second piezoelectric crystals fixed relative to the fixed ends of said first and second vanes, respectively; fourth and fifth means connected from said first and second crystals for producing a first and second square waves, respectively, at frequencies equal to those at the outputs of said crystals, said square waves both having the same amplitude; first and second amplifiers connected from said first power amplifier means connected from the outputs of both said fourth and fifth means to produce an output signal directly proportional to the algebraic sum of the amplitudes of the output signals of said fourth and fifth means; a driver coil connected from said power amplifier means to vibrate both of said vanes simultaneously; output means connected from the output of said power amplifier means to produce a signal of a magnitude directly proportional to the difference between the frequencies of the signals appearing at the outputs of said fourth and fifth means; and utilization means connected from said output means.
 25. The invention as defined in claim 24, wherein a capacitor is connected in series from the output of said power amplifier means to said driver coil.
 26. The invention as defined in claim 25, wherein sixth means are connected to said driver coil to supply a D.C. current thereto larger than the peak A.C. current produced therein by the varying output voltage of said power amplifier means.
 27. The invention as defined in claim 26, wherein said sixth means supplies a constant D.C. current to said driver coil.
 28. The invention as defined in claim 27, wherein said output Means includes an AM detector connected from the output, and a squarer connected from the output of said AM detector, and a frequency-to-voltage converter connected from the output of said squarer to said utilization means.
 29. The invention as defined in claim 28, including a voltage-to-current converter connected from the output of said frequency-to-voltage converter to the input of said utilization means, said utilization means including a milliammeter calibrated in gravity.
 30. The invention as defined in claim 26, wherein said output means includes an AM detector connected from the output, and a squarer connected from the output of said AM detector, and a frequency-to-voltage converter connected from the output of said squarer to said utilization means.
 31. The invention as defined in claim 24, wherein sixth means are connected to said driver coil to supply a D.C. current thereto larger than the peak A.C. current produced therein by the varying output voltage of said power amplifier means.
 32. The invention as defined in claim 31, wherein said output means includes an AM detector connected from the output, and a squarer connected from the output of said AM detector, and a frequency-to-voltage converter connected from the output of said squarer to said utilization means.
 33. The invention as defined in claim 25, wherein said output means includes an AM detector connected from the output, and a squarer connected from the output of said AM detector, and a frequency-to-voltage converter connected from the output of said squarer to said utilization means.
 34. The invention as defined in claim 24, wherein said output means includes an AM detector connected from the output, and a squarer connected from the output of said AM detector, and a frequency-to-voltage converter connected from the output of said squarer to said utilization means.
 35. Apparatus for producing an output which is a function of two gas densities, said apparatus comprising: a thermally conductive body defining first and second spaced internal chambers, said first chamber being closed except for an inlet port and a vent port in said body, said second chamber being closed except for a vent port in said body, said first and second chamber vent ports venting said first and second chambers, respectively, to ambient atmospheric pressure, said second chamber being filled with air, said body having a portion defining a passageway therein with an outlet in communication with said first chamber inlet port, said passageway having an inlet to receive a gas to be monitored, the portion of said body defining said passageway having a heat exchanger construction such that gas is caused to flow in said passageway in heat exchange relation with said body, the mass and thermal conductivity of said body being relatively large so that in combination with said heat exchange construction, the temperature of the gas which fills said first chamber through said inlet port thereof is maintained at a temperature substantially equal to that of the air in said second chamber; source means to supply gas to said passageway inlet at a pressure sufficiently low that the gas and air in said first and second chambers, respectively, are both maintained substantially at atmospheric pressure; first and second means mounted on said body in said first and second chambers, respectively, to produce first and second outputs, respectively, which are respective functions of the density of the gas in said first chamber, and the density of the air in said second chamber; and third means connected from the outputs of said first and second means for producing an electrical output signal which is directly proportional to the ratio of the density of the gas in said first chamber to the density of the air in said second chamber.
 36. The invention as defined in claim 35, wherein said passageway is a slot having a thickness small in comparison to both its width and its length, the outputs of said first, secoNd and third means all being electrical signals.
 37. The invention as defined in claim 36, including utilization means connected from the output of said third means.
 38. The invention as defined in claim 37, wherein said utilization means is an indicator adapted to read directly in said density ratio.
 39. The invention as defined in claim 35, including utilization means connected from the output of said third means.
 40. A gravitometer comprising: a body having a chamber therein to contain a fluid; a spring metal cantilevered vane mounted in said chamber, said vane having one end fixed relative to said body and a free end opposite thereof for immersion in said fluid, said free end being positioned to vibrate back and forth in predetermined directions without touching said body; first means mounted on said body and actuable to vibrate said vane as aforesaid; second means mounted contiguous to said vane in a manner to produce a first A.C. output signal of a first frequency equal to a resonant frequency of said vane; third means connected between said first and second means in a manner to cause said first means to be actuated in a manner to cause said vane to vibrate as aforesaid, at least one of said means including an amplifier, said vane and said first, second and third means forming a closed loop electromechanical oscillator in which the loop gain is adequate to sustain vibration of said vane continuously; source means for producing a second A.C. output signal of a second frequency, said second signal having a period directly proportional to a reference fluid density at the same temperature and pressure as the fluid in said chamber; and output means connected from said third and source means to produce a third A.C. output signal of a magnitude directly proportional to the difference between said first and second frequencies.
 41. The invention as defined in claim 40, wherein utilization means are connected from said output means to receive said third signal.
 42. The invention as defined in claim 41, wherein said utilization means includes a voltmeter calibrated in dimensionless units of the ratio of the density of fluid in said chamber to the density of said reference fluid at the same temperature and pressure.
 43. A densitometer comprising: a body having a chamber therein to contain a fluid; a spring metal ferromagnetic cantilevered vane mounted in said chamber, said vane having one end fixed relative to said body and a free end opposite thereof for immersion in said fluid, said free end being positioned to vibrate back and forth in predetermined opposite directions without touching said body, said directions being approximately parallel to the direction in which the vane thickness is measured; an electromagnetic driver including a coil, said electromagnetic driver being fixed relative to said body in a position to attract said vane free end when said coil is energized; a piezoelectric crystal fixed relative to and contiguous to said one vane end; amplifier means connected from said crystal to said coil to provide a closed loop electromechanical oscillator, said amplifier means causing vibration of said vane through energization of said coil at a frequency directly proportional to that appearing at the output of said crystal, said amplifier means having a gain adequate to sustain said vane vibration continuously; output means connected from said amplifier means to produce an output signal directly proportional to the density of said fluid; and utilization means connected from said output means, said output means producing an output signal approximately proportional to density Rho defined by Rho At + B where t 1/f, f being directly proportional to the frequency of vibration of said vane and A and B being constants.
 44. A densitometer comprising: a body having a chamber therein to contain a fluid; a spring metal ferromagnetic cantilevered vane mounted in said chamber, said vane haVing one end fixed relative to said body and a free end opposite thereof for immersion in said fluid, said free end being positioned to vibrate back and forth in predetermined opposite directions without touching said body, said directions being approximately parallel to the direction in which the vane thickness is measured; an electromagnetic driver including a coil, said electromagnetic driver being fixed relative to said body in a position to attract said vane free end when said coil is energized; a piezoelectric crystal fixed relative to and contiguous to said one vane end; amplifier means connected from said crystal to said coil to provide a closed loop electromechanical oscillator, said amplifier means causing vibration of said vane through energization of said coil at a frequency directly proportional to that appearing at the output of said crystal, said amplifier means having a gain adequate to sustain said vane vibration continuously; output means connected from said amplifier means to produce an output signal directly proportional to the density of said fluid; and utilization means connected from said output means, said output means producing an output signal approximately proportional to density Rho defined by Rho At B where t 1/f, f being directly proportional to the frequency of vibration of said vane and A and B being constants, said vane being approximately rectangular and having a substantially uniform thickness between two rectangular plane surfaces thereof, said vane thickness being substantially smaller than the length thereof, said vane thickness also being substantially smaller than the width thereof, said one vane end being bonded to a metal disc, said disc having a recess therein on the side thereof opposite the side to which said vane is bonded, the bottom surface of said recess being located a distance from said one vane end substantially less than the thickness of said disc, said crystal being bonded to said recess bottom surface approximately midway along the length of said one vane end. 